O*-algebra
In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by Borchers (1962)[1] and Uhlmann (1962),[2] who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quantum field theory. Powers (1971)[3] and Lassner (1972)[4] began the systematic study of algebras of unbounded operators.
References
- ^ Borchers, H. -J. (April 1962). "On structure of the algebra of field operators". Il Nuovo Cimento. 24 (2): 214–236. doi:10.1007/BF02745645. ISSN 0029-6341.
- ^ Uhlmann, Armin (1962), "Über die Definition der Quantenfelder nach Wightman und Haag", Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Nat. Reihe, 11: 213–217, MR 0141413
- ^ Powers, Robert T. (June 1971). "Self-adjoint algebras of unbounded operators". Communications in Mathematical Physics. 21 (2): 85–124. doi:10.1007/BF01646746. ISSN 0010-3616.
- ^ Lassner, G. (December 1972). "Topological algebras of operators". Reports on Mathematical Physics. 3 (4): 279–293. doi:10.1016/0034-4877(72)90012-2.
Further reading
- Borchers, H. J.; Yngvason, J. (1975), "On the algebra of field operators. The weak commutant and integral decompositions of states", Communications in Mathematical Physics, 42 (3): 231–252, Bibcode:1975CMaPh..42..231B, doi:10.1007/bf01608975, ISSN 0010-3616, MR 0377550
- Schmüdgen, Konrad (1990), Unbounded operator algebras and representation theory, Operator Theory: Advances and Applications, vol. 37, Birkhäuser Verlag, doi:10.1007/978-3-0348-7469-4, ISBN 978-3-7643-2321-9, MR 1056697